# Thread: Prove recurrance relation

1. ## Prove recurrance relation

Prove the recurrence relation d/dx Hn(x) = 2nH(n−1(x)) for n = 0, 1, 2, ..

I think this has something to do with differentiating the generating function, maybe? But i can't see how it would work.

Thanks

2. Are those the Hermite polynomials?

3. yes they are

4. Ah. In that case, I'd go for the Rodriguez representation. Are you doing the probability version, or the physics version of the Hermites?

5. Physics. I know the form of rodriguez representation. But i dont understand how that can be used to answer my question?
Thanks

6. Why don't you just try differentiating it and see what happens?

7. I have done so, but i can't get anything that resembles the RHS, im left with:

(-1)^2 exp(x^2) (2x+1) + exp(-x^2) (d^n+1/dx^n+1 + d^n/dx^n).

Any idea? thanks

8. Look at this thread. It works out if you take the derivative correctly, which I'm not sure you did.

9. ahhh i see how, using the identity on that thread.

Thanks

10. You're welcome. Have a good one!